7th Maths : Term 2 Unit 3 : Algebra : Exercise 3.4 : Miscellaneous Practice problems, Challenge Problems, Text Book Back Exercises Questions with Answers, Solution

**Exercise
3.4**

__Miscellaneous
Practice problems__

**1.
6 ^{2}× 6^{m} = 6^{5}, find the value of ‘m’.**

6^{2+m} = 6^{5}

Base are equal. So powers also equal.

2 + m =5

m = 5–2 = 3

m = 3

** **

**2.**** ****Find the unit digit of 124 ^{128}
**

Unit digit of base 124 is 4 and power is 128 (Even number).

So, the unit digit of 124^{128} is 6.

Unit digit of base 126 is 6 and power is 124 (Even number).

So, the unit digit of 126^{124} is 6.

6 × 6 = 36, Unit digit of 36 is 6.

So, Unit digit of 124^{128} × 126^{124 }is 6.

** **

**3.**** ****Find the unit digit of the numeric expression:
16 ^{23} **

Unit digit of base 16 is 6 and power is 23 (Odd number).

So, the unit digit of 16^{23} is 6.

Unit digit of base 71 is 1 and power is 48 (Even number).

So, the unit digit of 71^{48} is 1.

Unit digit ofbase 59 is 9 and power is 61 (Odd number).

So, the unit digit of 59^{61} is 9.

Adding Unit digits, 6+1+9 = 16, Unit digit of 16 is 6.

So, unit digit of 16^{23} + 71^{48} + 59^{61}
is 6.

** **

**4.**** ****Find the value of _{ }**.

**[ ****(**** ****−****1****)**^{6}** ****×**** ****(**** ****−****1****)**^{7}** ****×**** ****(**** ****−****1****)**^{8}** ]
/ [ ****(**** ****−****1****)**^{3}** ****×**** ****(**** ****−****1****)**^{5
}**]**

[ (–1)^{6} × (–1)^{7 }× (–1)^{8} ] / [ (–1)^{3
}× (–1)^{5 }]

(–1)^{6} = 1, (–1)^{–1} = –1, (–1)^{8} =
l, (–1)^{3} = –1, (–1)^{5} = –1

[ (–1)^{6 }×^{ }(–1)^{7} × (–1)^{8} ] /^{ }[ (–1)^{3} × (–1)^{5
}]^{ }= [ 1 × (–1) ] / [ (–1) × (–1)^{ }] = (–1) / 1 = –1

** **

**5.**** ****Identify the degree of the expression,
2 a ^{3}bc **

Degree of 2a^{3}bc is 5

Degree of 3a^{3}b is 4

Degree of 3a^{3}c is 4

Degree of 2a^{2}b^{2}c^{2} is 6

The degree of the expression is 6.

** **

**6.**** ****If p **

p = –2, q = l, r = 3

3p^{2}q^{2}r = 3(–2)^{2 }(1)^{2}
× 3

= 3 × 4 × 1 × 3 = 36

** **

__Challenge
Problems__

** **

**7. LEADERS
****is
a WhatsApp group with 256 members. Every one of its member is an admin for their own WhatsApp group with
256 distinct members. When a message is posted in LEADERS and everybody forwards
the same to their own group, then how many members in total will receive that message?**

Number of WhatsApp group members = 256

Number of members in each group = 256

Number of members in total will receive that message = 256 × 256

Number of members in total will receive that message = 65536

** **

**8.
Find x such that 3^{x} **

3^{x} + 3^{2 }–3*x* = 216

3^{x} + 9 –3*x* =
216

3^{x }(9–1) = 216

3^{x} × 8 = 216

3^{x} = 216 / 8 = 27 = 3^{3 }

3^{x }= 3^{3}

Bases are equal.

So, the powers also equal.

x = 3.

** **

**9.
If X ****=**** 5 x ^{2} **

X = 5x^{2} + 7x + 8

Y = 4x^{2 }– 7x + 3

X + Y = 9 x^{2} +11

The degree of X+Y is 2.

** **

**10.
Find the degree of ****(**** 2 a ^{2} **

__2a ^{2} + 3ab –b^{2} – 3a^{2}__ + ab + 3b

__2a ^{2} – 3a^{2} + 3ab + ab__ – b

–a^{2} + 4ab + 2b^{2}

The degree of the expression is 2.

** **

**11.
Find the value of w, given that x **

w = x^{2} –y^{2} + z^{2} –xyz

w = (3)^{2} – (4)^{2 }+ (–2^{)2} – 3 × 4
× –2

= 9 – 16 + 4 + 24

= 9 + 4 + 24 – 16

= 37 – 16 = 21

** **

**12.
Simplify and find the degree of 6 x ^{2} **

6x^{2} + 1 – [8x– {3x^{2 }–7 – (4x^{2 }–
2x + 5x + 9)}]

6x^{2 }+ 1 – [8x –3x^{2} + 7 + (4x^{2} –2x
+ 5x + 9)]

6x^{2} + 1 – 8x + 3x^{2} –7 – (4x^{2} +
2x –5x –9)

6x^{2} + 3x^{2 }– 4x^{2 }–8x – 5x + 2x+
1–7–9

5x^{2} – 13x + 2x + 1 –16

5x^{2} –11x –15

The degree of the expression is 2.

** **

**13.
The two adjacent sides of a rectangle are 2 x^{2} **

The two adjacent sides,

Length l = 2x^{2 }–5xy + 3z^{2}

Breadth b = 4xy –x^{2 }–z^{2}

Perimeter = 2(l + b)

= 2(2x^{2 }– 5xy + 3z^{2 }+ 4xy – x^{2 }–
z^{2})

= 2(x^{2} – xy + 2z^{2})

Perimeter of the rectangle = 2x^{2 }– 2xy + 4z^{2 }

The degree of the Perimeter is 2.

__ANSWERS:__

**Exercise 3.4**

1.* m *= 3

2. 6

3. 6

4. −1

5. 6

6. 36

**Challenge problems **

7. 65536

8.* x *= 3

9. 2

10. 2

11. 21

12. 5* x*^{2} − 11*x* − 5 ; 2

13. 2*x*^{2} − 2xy + 4*z*^{2} ; 2

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7th Maths : Term 2 Unit 3 : Algebra : Exercise 3.4 | Questions with Answers, Solution | Algebra | Term 2 Chapter 3 | 7th Maths

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